A failure to place controls on the number of students enrolling for higher learning qualifications at scores of private colleges has left an £80m shortfall in the budget of the Department for Business this year, a deficit that is forecast to soar to a third of a billion pounds in the next two years.

The number of students enrolling for higher national diplomas (HNDs) and certificates (HNCs) at 46 private colleges has ballooned from 13,000 during 2011-12 to 30,000 in the last academic year.

The budget shortfall, revealed in internal forecasts at Vince Cable's department seen by the Guardian, has come about because it has to spend money on providing financial support to students in the form of grants and loans. Students can receive well over £10,000 in support over a typical two-year course.

Four in 10 of those receiving financial support to study for HNDs and HNCs are from overseas – compared with 5% for publicly funded higher education in general. Fearing possible fraud and eager to scale back expenditure, the business department has in the last few weeks stopped HND and HNC grants and loans going to about 5,000 Romanians and Bulgarians, suspended funding payments to one college, and is this week sending letters to 23 of the fastest growing privately run colleges in England telling them not to admit more students than they had registered on official surveys last year.

One expert warned the overspend was as a result of ministers "running an experiment with no proper controls in place". Andrew McGettigan, author of The Great University Gamble: Money, Markets and the Future of Higher Education, said that there was too much emphasis on trying to create a market in higher education provision.

He added that it would be difficult now to rein the sudden expansion in places because they had already been given permission to open their doors to students: "Once these private providers are approved [by the department] they can recruit as many students as they can. It's a deliberate policy to shake things up."

Internal departmental forecasts seen by the Guardian suggest the number of students studying HNDs and HNCs at the private institutions will increase by a third – to 40,000 for this coming academic year. By 2015-16 the "budget pressure" caused by the extra numbers is forecast to rise to £330m. A BIS spokesperson said: "Planned recruitment at some [private] providers was unaffordable."

A spokesperson added: "Our goal has always been to create a higher education sector that responds to student demand and has the ability to expand and create more competition. But we've always been clear that we have a responsibility to keep control of public finances and minimise the risk of unsustainable growth and budget, which is why we confirmed our intention to introduce students number controls from 2014/15."

"We've written to 23 private providers to instruct them to stop recruitment for HND/C's for the remainder of 2013/14 so that we will be focussing funding mainly towards degree level qualifications this year."

So big is the overspend that the business department has had to propose cuts of £25m to the Access to Learning hardship fund, which provides financial support for students, and £20m from budget spent on higher education teaching to help balance the books in the next financial year. One insider added: "We're only realising now the size the blank cheque we've written to private providers."

To qualify for fee loans of up to £6,000 and other payments to aid with living costs, EU nationals must be resident in the wider European economic area for at least three years. Departmental guidance states that without the right to settle in the EU until 2007, Romanians and Bulgarians will find it harder to qualify for fee and maintenance loans worth thousands of pounds. But more than 25% of those whose loans have been halted have already replied to requests for more evidence of their resident status. One internal memo admits: "Entrance criteria to study these qualifications are far less stringent than those for full degrees."

A letter to Mick Laverty, chief executive of the Students Loan Company, from Matthew Hilton, senior director of higher education at BIS, raises concerns about the checks on foreign students. "There may be perfectly legitimate reasons for this, but as the weaknesses identified in the residency check process for Romanian and Bulgarian students may also be exploited by students from other European nationals, these numbers are cause for concern".

But Remus Pricopie, the Romanian minister of national education said, "According to EU regulations, a student from a European Union country has the right to study in any other EU country in the same conditions as the students from the hosting country."

Liam Byrne, the shadow higher education minister, said: "We need some big answers fast for how this government has let spending balloon out of control – and students now need assurances that they won't be paying the price for this government's incompetence."

David Willetts, the universities and science minister, said HNDs and HNCs were "well respected" qualifications. He added:"We are instructing the providers that are growing most rapidly to stop recruiting students to these courses for this year."